In most states, a popular vote tie is broken by a coin toss or drawing
names from a hat. The odds of a many-state tie are slimmer than the odds
of the hat being hit by a bale of cocaine dumped from a drug-smuggling
airplane.

Nate Silver flippantly posted his 'tie' question on Twitter during the
tallying of the extremely close 2012 Republican Iowa Caucus results. In
that case, an exact tie was averted—Santorum ended up winning by 34
votes out of 121,503. And since it was a non-binding nominating vote,
the Iowa Republican Party could handle a tie any way they wanted.

But since it’s Election Day, let’s apply his question to the current
contest. What will happen if there's a tie?

I don't mean an electoral college tie. There’s probably about a 1 in 500
chance of one of those this year, and the consequences are thoroughly
explored.
Instead, the question concerns both candidates getting the same number
of votes in a state.

Several researchers—including Silver
himself—have
calculated the odds of a state winner being decided by a single vote,
which is effectively the same as the probability of a tie vote. For
typical close states, the linked article calculates the probabilities to
be in the neighborhood of 1 in 100,000—which makes intuitive sense,
since 100,000 is the sort of vote margin by which swing state elections
are typically decided.

So what if there's a tie in a close state this year?

For that matter, what if there’s a tie in every battleground state?

Well, for starters, recounts happen. But since recounts happen in close
elections in general, these are just as likely to create ties as to
break them. They don’t change the underlying probability. So let’s
assume that after all recounts, there’s a tie. What then?

“Drawing lots” can mean a coin toss, drawing straws, or picking a name
from a hat. Most states leave the details up to the Secretary of State
or an electoral board, although Iowa Code 50.44 specifies that the names
be written on pieces of paper and placed in a “receptacle”. In North
Carolina, however, a tie vote (when more than 5,000 votes are cast)
results in a new election. (Which could potentially itself result in a
tie ...)

But let’s imagine that there’s not just one state that’s tied—instead,
the nine most competitive states are tied (and the rest go as
expected). If North Carolina held a runoff to break the tie, and the
other eight states flipped coins (or picked from Iowa’s receptacle),
Obama would be reelected in 431 out of 512
cases—about
84% of the time.

But how likely is a nine-state tie?

If we ballpark the odds of a tie vote in each close state at 1 in
100,000, then the odds of a tie vote in all nine states is in the
neighborhood of one in a quattuordecillion—1 followed by 45 zeroes.
(This ignores vote correlation between states, but it’s good enough for
a first-order estimate).

Florida is hit by an average of 66 tornadoes per
year.
If each tornado is 50 yards wide and has a path 1.5 miles long (which is
typical, if not
necessarily the mean), we can calculate that a typical location in
Florida experiences an average 1.4 picotornados per second:

Astronomer Alan Harris calculates that a person’s lifetime odds of death
from a comet or meteorite impact are about 1 in 700,000. If a typical
person in the calculation lives 70 years, this suggests a Florida
resident suffers an average of 0.64 femtodeaths per second from
meteorite impacts:

(By the way—this means that given a street price of $20,000 per
kilogram, a typical acre of Florida land produces an average revenue of
three cents per year in falling cocaine bales).

Putting all this together: The probability that every battleground state
is exactly tied is roughly equal to the probability that, when one of
the Florida electors reaches into the hat to draw a name, he or she is
struck by a falling cocaine bale, the hat is hurled away within the next
few seconds by a tornado, and the elector is obliterated minutes later
by a meteorite impact.

If you’re in the US, don’t forget to vote—your vote could make or break
a tie.